Multiple questions (mesh/3d view)
I'm unfortunately unable to answer your first questions. Hopefully someone else can explain for you in more detail how that works.

Regarding the keybindings, I have a solution for you. If you don't use all of the standard shortcuts to change Methods to display/shade objects in 3D view, you can easily change one of those shortcuts:


Go to File > User Preferences...
Go to the Input tab
In the list, open 3D View > 3D View (Global)
Scroll down to Context Toggle Values (there should be three of them)
Open one of them that you don't use
Change the bottom Value to MATERIAL (keep the first SOLID if you want to be able to toggle between them)
Click on Save User Settings


If you use all of the shortcuts under Context Toggle Values, then continue from step 3:


Scroll all the way down to the last shortcut in 3D View (Global) and click on Add New
Open your new shortcut (named none)
In the box that says none, type wm.context_toggle_enum and press Enter. The RNA box should have changed to WM_OT_context_toggle_enum
In the Context Attributes box, type space_data.viewport_shade
In the upper Value box, type SOLID
In the lower Value box, type MATERIAL
Set the shortcut to whatever you like. I would suggest Ctrl+Shift+Alt+Z, to not interfere with undoing/redoing (press on the button that says A and check the checkboxes for Shift, Ctrl and Alt)
Click on Save User Settings


And that's it! (I've tested this with Blender version 2.76b.)